Most do not consider Israel to ever have been a world power or even to have had that as an aspiration. After all, the promise to Abraham was not world domination but blessing. That said, Israel reached its peak on the world political stage under Solomon who also led to its decline.

The kingdom established by David on the foundations started by Saul and Samuel attained all the borders and limits of the Biblical Promised Land. These borders were kept by Israel through the time of David and Solomon. More than this, all of the Near East was under the control of the united tribes of Israel and ruled from Jerusalem. Garrisons of Israeli soldiers were stationed in Damascus, Hamath, Ammon, Edom, Moab and the out posts of the Negev and the Euphrates River. Shipping in the Mediterranean and Indian Ocean was under the control of Israel. Coincidentally the strongest nations of the Near East, Egypt, Assyria, Babylon, were eclipsed by the power of Israel and due to Israel's political power and control this period is an empty page in the annals of those subject nations. (http://www.moellerhaus.com/assyrian.htm 12/14/13).

In the Bible story it is faithfulness to God that is the driver and measure of the story. We see the influence of Israel decline with the decline in the faithfulness of the King. (When Solomon started relying on foreign alliences rather than God.) This is the issue is driven home in the Books of Kings and as the faithfulness of the nation declines it leads to the eventual judgment on the nation. There is a faithful remnant that are preserved through the exiles and have been able to reconstitute a nation state periodically in history. 

This is the story in the following time line. There are many who say that dates before the time of David cannot be stated with any certainty. The bulk of the dates are from the Jewish site referenced below and represent the Bible's internal chronology.

 

Date Event
  The Formation of Israel – the story of the Patriarchs
1812 BC Abraham
1712 BC Isaac
1652 BC Jacob
1428 BC Egyptian Bondage
1312 BC Moses and the Exodus
1272 BC Joshua and the conquest of the Promised land 
1106 BC Judges
  Monarchy
879 BC Saul
877 BC David
836 BC Solomon
c 855 - 607 BC Assyrian Empire rising – from the first temple through the fall of Samaria in the north
796 BC Divided Kingdom
555 BC Assyrians overrun Northern Tribes
547 BC Sennacherib (King of Assyria) attacks Jerusalem (beginning of the end for the kingdom of Juda.)
  Babylonians overrun Assyrian Empire – the time of Daniel and the prophets
422 BC Babylonians conquer Judah and destroy Temple
  Persians overrun Babylonians
  The Remnant returns from Exile – Ezra-Nehemiah
370 BC Jews begin to return from Babylonian exile
355 BC The book of Esther – the Miracle of Purim
352 BC Construction of Second Temple Begins - this temple is expanded and completed under the Herodeans and destroyed shortly thereafter.
  Greeks Overrun Persian Empire
312 BC Greeks Conquer Israel
245 BC Septuagint (Hebrew writings in Greek)
167 BC Revolt of the Maccabees - Recorded in the books of the Maccabees
146 BC Romans Conquer the Greeks
140 - 116 BC Hasmonean Dynasty
139 BC Miracle of Hanukah - Recorded in the Talmud - The history of these events is recorded in the books of Maccabees.
63 BC Rome invades Israel
47 BC - AD 100 Herodian Dynasty
37 BC Herod the Great begins his rule. According to Josephus, Herod ruled for 37 years, 34 of them after capturing Jerusalem.
4 BC - 33 Life and Ministry of Jesus
6 AD Iudaea (Judea, Samaria and Edom) is a provence of Rome
26 - 36 Pontius Pilate - Roman Prefect
41 - 44 Nominal Autonomy under Harod Agripa
66 - 136 The Jewish-Roman Wars - A series of three Jewish revolts in an attempt to restore an independent Judean state.
66-73 The Great Revolt of the Jews against Rome (First Jewish War)
70 Jerusalem conqurred by Rome and the second (Herod's) Temple is destroyed
115 - 117 Kitos War (Second Jewish War)
120 Bar Kochba rebellion (Third Jewish War)
135 Hadrian changes the name of the province from Iudaea to Syria Palaestina and Jerusalem became Aelia Capitolina which Hayim Hillel Ben-Sasson states was done to erase the historical ties of the Jewish people to the region.
   
219 Mishna compiled - Rabbi Yahuda HaNasi - Mishna whech means "study by repetition" is the first compilation of the "Oral Torah" in written form. It is also the first major work of Rabbinic literature.
476 Fall of the City of Rome, The Byzantine Empire continues in the East
   
638 Islamic conquest of Jerusalem
1096 Crusades Begin
1135 Maimonides - Rambam (from "Rabbeinu Moshe Ben Maimon")
1348 The black plague
1478 Inquisition(s)
1492 Jews Expelled from Spain
  Ottoman Empire takes over Middle East
962 - 1806 Holy Roman Empire (Rebirth if the Western Roman Empire in Europe)
1517 Protestant reformation
1914 - 1918 World War I
  End of Ottoman empire
1920 - 1948 British mandate - After the end of World War I
1939 - 1945 World War II
1948 Modern State of Israel

 

 http://www.simpletoremember.com/articles/a/timeline_from_abraham_to_the_founding_o/  11/17/13

http://en.wikipedia.org/wiki/Mandatory_Palestine 3/23/14

http://en.wikipedia.org/wiki/Judea_(Roman_province) 3/23/14